As soon as you expand to the place, it should appear in your inventory. If not, you have to complete the entire goal before they put it there.
Search your inventory under Decorations.
Otherwise, this is what a contributor wrote about it: [NOTE] The disappearance of Mt. Fuji after a player has expanded to it AND completing the Climb Mount Fuji! goal is a known issue. Please contact Zynga support and they will add Mt. Fuji to your inventory.
Well, then I'd click the zynga support link I gave, and tell them that the game didn't give you Mt. Fuji even though you'd completed the whole goal. They;ll put one in your inventory - after a few days, usually.